We consider a numerical method to verify the existence and uniqueness of the solutions of nonlinear hyperbolic problems with guaranteed error bounds. Using a C 1 nite element solution and an inequality constituting a bound on the norm of the inverse operator of the linearized operator, we numerically construct a set of functions which satisfy the hypothesis of Banach's xed point theorem for a c...

The force-based quasicontinuum (QCF) approximation is the principle that lies behind the most commonly used atomistic/continuum hybrid models for crystalline solids. Recent analyses have shown some potential pitfalls of the QCF method, particularly the lack of positive definiteness of the linearized QCF operator and the lack of uniform stability as the number of atoms tends to infinity. We deri...

In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We deene local ill-posedness of a nonlinear operator equation F(x) = y 0 in a solution point x 0 and the interplay between the nonlinear problem and its linearization using the Fr echet derivative F 0 (x 0). To nd an appropriate ill-posedness concept for 1 the linearized equation ...

In this paper an observability analysis is performed for an axial dispersion tubular bioreactor that involves one nonlinear growth reaction. The process is described by a semilinear parabolic Partial Differential Equation (PDE). More precisely, the analysis is performed on a tangent linearized model, that is described by a linear PDE with a spatial-dependent coefficient. It is reported that the...

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse time migration (RTM). In the process, the explicit evaluation of the so-called normal operator is avoided, while other differential and pseudodifferential operator factors are introduced. We prove that, under certain conditio...

We characterize the dependence on doublets of the cohomology of an arbitrary nilpotent differential s (including BRST differentials and classical linearized Slavnov-Taylor (ST) operators) in terms of the cohomology of the doublets-independent component of s. All cohomologies are computed in the space of local integrated formal power series. We drop the usual assumption that the counting operato...

This paper considers the analysis and control of fluid flows using tools from dynamical systems and control theory. The employed tools are derived from the spectral analysis of various linear operators associated with the Navier–Stokes equations. Spectral decomposition of the linearized Navier-Stokes operator, the Koopman operator, the spatial correlation operator and the Hankel operator provid...

where Sn is the unit sphere {(η,ξ) ∈R×Rn : η2 +‖ξ‖2 = 1} in Rn+1 and σn is the surface measure on Sn normalized to have total measure one. This operator plays an important role and has many applications, for example, in image processing of so-called synthetic aperture radar (SAR) data (see [7, 8]), or in the linearized inverse scattering problem in acoustics [6]. In [10], the authors associate ...

In the present paper, we establish existence and orbital instability results of cnoidal periodic waves for quintic Klein-Gordon nonlinear Schrödinger equations. The spectral analysis corresponding linearized operator is established by using Floquet theory. determined applying an abstract result due to Shatah Strauss.

The ability of linear controllers to stabilize the conduction (no-motion) state of a saturated porous layer heated from below and cooled from above is studied theoretically. Proportional, suboptimal robust(H∝) and linear quadratic Gaussian (H2) controllers are considered. The proportional controller increases the critical Rayleigh number for the onset of convection by as much as a factor of 2. ...